12-267/Topic List
Here is a (incomplete) list of subjects covered in MAT267 this semester.
First-order linear equations
The brachistochrone
Separable equations
Escape velocities
Changing source and target coordinates
Homogeneous equations
Reverse-engineering separable and exact equations
Solving exact equations with and without integration factors
Calculus of Variations
Chain law
Euler-Lagrange, derivation (alternate) and reductions
Lagrange multipliers
Isoperimetric Inequality
Numerical methods
Examples and derivations
Evaluating local error
Higher Order Constant Coefficient Homogeneous Linear ODEs
Multiple roots
Reduction of order
Method of Undetermined Coefficients
Systems of First-Order Linear Equations
Matrix exponetiation
Phase portraits
Non-homogeneous systems
Power-series solutions
Global existence for linear ODEs
Wronskian
Series solutions for y' = f(x,y)
Radius of convergence
Qualitative Analysis
Airy's equation
Fuch's Theorem
Regular singular points
Frobenius series and Frobenius Method
The basic oscillation theorem
Non-oscillation theorem
Sturm comparison theorem
Changing the independent variable
Amplitudes of oscillations
